A theory of spatial propagation of turbulence, referred to as turbulence spreading, is developed for the two-field model of drift wave turbulence. Markovian closure expressions for the flux of kinetic and internal fluctuation energies are systematically derived. Simplified closure expressions are used to obtain two coupled reaction-diffusion equations for kinetic and internal energy. The efficacy of various nonlinear interaction mechanisms for spreading is analyzed systematically. Spreading of internal energy is predicted to “lead” that of kinetic energy. The important role of zonal flow damping in spreading is identified, but zonal flows are shown not to be the dominant agents of turbulence spreading.

The reduction in the transport of particles and heat by a strong mean shear flow is studied, in the context of interchange and ion-temperature gradient turbulence models. Compared to passive scalar transport, a stronger reduction in the transport (scaling with the shearing rate Ω as αΩ -3 in Ω) results from a severe reduction in the amplitude of turbulent velocity in both models. However, the cross phase is only modestly reduced, as in the scalar field case. These results are in qualitative agreement with the results from both gyrokinetic and gyrofluid simulations of toroidal ion-temperature gradient turbulence [Lin et al., Phys. Rev. Lett. 83, 3645 (1999); Falchetto and Ottaviani, Phys. Rev. Lett. 92, 025002 (2004)], but contradict recent claims in some literature, highlighting the importance of the detailed properties of the flow in determining the overall transport level. © 2004 American Institute of Physics,.

We present the results of a derivation of the fluctuation energy transport matrix for the two-field Hasegawa-Wakatani model of drift wave turbulence. The energy transport matrix is derived from a two-scale direct interaction approximation assuming weak turbulence. We examine different classes of triad interactions and show that radially extended eddies, as occurs in penetrative convection, are the most effective in turbulence spreading. We show that in the near-adiabatic limit internal energy spreads faster than the kinetic energy. Previous theories of spreading results are discussed in the context of weak turbulence theory.

A physical model of turbulent equipartition (TEP) of plasma angular momentum is developed. We show that using a simple, model insensitive ansatz of conservation of total angular momentum, a TEP pinch of angular momentum can be obtained. We note that this term corresponds to a part of the pinch velocity previously calculated using quasilinear gyrokinetic theory. We observe that the nondiffusive TEP flux is inward, and therefore may explain the peakedness of the rotation profiles observed in certain experiments. Similar expressions for linear toroidal momentum and flow are computed and it is noted that there is an additional effect due the radial profile of moment of inertia density.

Spreading of turbulence as a result of nonlinear mode couplings and the associated spectral energy transfer is studied. A derivation of a simple two-field model is presented using the weak turbulence limit of the two-scale direct interaction approximation. This approach enables the approximate overall effect of nonlinear interactions to be written in the form of Fick's law and leads to a coupled reaction-diffusion system for turbulence intensity. For this purpose, various classes of triad interactions are examined, and the effects that do not lead to spreading are neglected. It is seen that, within this framework, large scale, radially extended eddies are the most effective structures in promoting spreading of turbulence. Thus, spectral evolution that tends toward such eddies facilitates spatial spreading. Self-consistent evolution of the background profile is also considered, and it is concluded that the profile is essentially slaved to the turbulence in this phase of rapid evolution, as opposed to the case of avalanches, where it is the turbulence intensity that would be slaved to the evolving profile. The characteristic quantity describing the evolving background profile is found to be the mean "potential vorticity" (PV). It is shown that the two-field model with self-consistent mean PV evolution can be reduced to a single Fisher-like turbulence intensity transport equation. In addition to the usual nonlinear diffusion term, this equation also contains a "pinch" of turbulence intensity. It is also noted that internal energy spreads faster than kinetic energy because of the respective spectral tendencies of these two quantities. © 2007 American Institute of Physics.

Abstract: This paper presents a mechanism for enhanced regulation of drift wave turbulence by zonal flows in the presence of a fast ion population. It demonstrates that dilution effects due to the energetic particles (EPs) have a far-reaching impact on all aspects of the nonlinear dynamics. The modulational growth of zonal flow shear and the corresponding evolution of drift wave energy are calculated with dilution effects. The coupled zonal flow growth and drift wave energy equations are reduced to a predator–prey model. This is solved for the fixed points, which represents the various states of the system. Results display a strong dependence on dilution, which leads to greatly reduced levels of saturated turbulence and transport. Implications for the FIRE mode plasma of KSTAR are discussed in detail. This model is perhaps the simplest dynamical one which captures the beneficial effects of EPs on confinement.

The effect of Alfvén waves on turbulent momentum transport is studied in three-dimensional reduced magnetohydrodynamic turbulence. A strong external uniform magnetic field B0 is assumed to be present orthogonal to both background shear flow and its inhomogeneity. Energy is injected into the fluid and/or magnetic field on small scales. It is shown analytically that eddy viscosity is reduced as 1/B20 for a strong B0, due to the cancellation of the Reynolds stress by Maxwell stress. The sign of eddy viscosity is found to depend on the detailed properties of forcings. Specifically, it is positive for fluid forcing but depends on the anisotropy of the forcing in the case of magnetic forcing. Furthermore, it is indicated that a magnetic field tends to laminarize a mean shear flow. The possible implication of these results for the dynamics of the zonal flows in tokamaks is discussed in view of the cancellation of stresses. © 2001 American Institute of Physics.

We present a paradigm for the generation of small scale coherent vortex (SSCV) in drift wave-zonal flow (DW-ZF) turbulence. We demonstrate that phases of DWs can couple coherently, mediated by the ZF shearing. A SSCV is formed when the phases of the DWs are "attracted" to form a stable "phase cluster." We show that the ZF shearing induces asymmetry between "attractive" and "repulsive" phase couplings, so that a net attractive phase coupling results. The turbulent DWs will (partially)synchronize into a stable SSCV at locations, where the attractive phase coupling induced by the ZF shearing exceeds the "detuning" effects by the DW dispersion and random phase scattering. We also discuss the "self-binding" effect of the newly formed SSCV.

A novel mechanism for the generation and amplification of intrinsic rotation at the low-mode to high-mode transition is presented. The mechanism is one where the net parallel flow is accelerated by turbulence. A preferential direction of acceleration results from the breaking of k∥ →- k∥ symmetry by sheared E×B flow. It is shown that the equilibrium pressure gradient contributes a piece of the parallel Reynolds stress, which is nonzero for vanishing parallel flow, and so can accelerate the plasma, driving net intrinsic rotation. Rotation drive, transport, and fluctuation dynamics are treated self-consistently. © 2007 American Institute of Physics.